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We study the p-fractional optimal design problem under volume constraint taking special care of the case when p is large, obtaining in the limit a free boundary problem modeled by the Hölder infinity Laplacian operator. A necessary and sufficient condition is imposed in order to obtain the uniqueness of solutions to the limiting problem, and, under this condition, we find precisely the optimal configuration for the limit problem. We also prove the sharp regularity (locally C 0 ,s) for any limiting solution. Finally, we establish some geometric properties for solutions and their free boundaries. © 2018 American Mathematical Society.


Documento: Artículo
Título:The limit as p →∞ in free boundary problems with fractional p-laplacians
Autor:DA SILVA, J.V.; Rossi, J.D.
Filiación:FCEyN, Department of Mathematics, Universidad de Buenos Aires, Ciudad Universitaria-Pabellón I, Buenos Aires, C1428EGA, Argentina
Palabras clave:Fractional diffusion; Hölder infinity laplacian; Optimal design problems; Sharp regularity
Página de inicio:2739
Página de fin:2769
Título revista:Transactions of the American Mathematical Society
Título revista abreviado:Trans. Am. Math. Soc.


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---------- APA ----------
DA SILVA, J.V. & Rossi, J.D. (2019) . The limit as p →∞ in free boundary problems with fractional p-laplacians. Transactions of the American Mathematical Society, 371(4), 2739-2769.
---------- CHICAGO ----------
DA SILVA, J.V., Rossi, J.D. "The limit as p →∞ in free boundary problems with fractional p-laplacians" . Transactions of the American Mathematical Society 371, no. 4 (2019) : 2739-2769.
---------- MLA ----------
DA SILVA, J.V., Rossi, J.D. "The limit as p →∞ in free boundary problems with fractional p-laplacians" . Transactions of the American Mathematical Society, vol. 371, no. 4, 2019, pp. 2739-2769.
---------- VANCOUVER ----------
DA SILVA, J.V., Rossi, J.D. The limit as p →∞ in free boundary problems with fractional p-laplacians. Trans. Am. Math. Soc. 2019;371(4):2739-2769.